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[PATCH] Implement fma correctly


Hi!

This patch fixes a bug in fmaf (the union is for double, not float,
so Inf/NaN test is exponent == 0x7ff instead of == 0xff) and implements
fma (both using just double arithmetics, where I hope I got the overflow
checks right) and for IEEE quad using long double arithmetics.
Tested on x86_64-linux, it is very well possible it won't work correctly
on i686 due to excess precision.  For i686 we could add a -mfpmath=sse -msse2
compiled version as yet another ifunc variant for SSE2+ and then have some
excess precision safe variant (e.g. doing the computation using 80-bit
long double somehow - we wouldn't need to deal with overflows then, but
we'd need to figure out how to do the rouding properly).

2010-10-12  Jakub Jelinek  <jakub@redhat.com>

	[BZ #3268]
	* math/libm-test.inc (fma_test): Add some more fmaf tests, add
	fma tests.
	* sysdeps/ieee754/dbl-64/s_fmaf.c (__fmaf): Fix Inf/Nan check.
	* sysdeps/ieee754/dbl-64/s_fma.c: New file.
	* sysdeps/i386/i686/multiarch/s_fma.c: Include
	sysdeps/ieee754/dbl-64/s_fma.c instead of math/s_fma.c.
	* sysdeps/x86_64/multiarch/s_fma.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/s_fma.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_fma.c: New file.

--- libc/math/libm-test.inc.jj	2010-10-12 07:36:10.000000000 +0200
+++ libc/math/libm-test.inc	2010-10-12 20:36:13.000000000 +0200
@@ -2789,9 +2789,19 @@ fma_test (void)
   TEST_fff_f (fma, minus_infty, minus_infty, minus_infty, nan_value, INVALID_EXCEPTION);
 
   TEST_fff_f (fma, 1.25L, 0.75L, 0.0625L, 1.0L);
-#ifdef TEST_FLOAT
+#if defined (TEST_FLOAT) && FLT_MANT_DIG == 24
   TEST_fff_f (fma, 0x1.7ff8p+13, 0x1.000002p+0, 0x1.ffffp-24, 0x1.7ff802p+13);
   TEST_fff_f (fma, 0x1.fffp+0, 0x1.00001p+0, -0x1.fffp+0, 0x1.fffp-20);
+  TEST_fff_f (fma, 0x1.fffffep+127, 0x1.001p+0, -0x1.fffffep+127, 0x1.fffffep+115);
+  TEST_fff_f (fma, -0x1.fffffep+127, 0x1.fffffep+0, 0x1.fffffep+127, -0x1.fffffap+127);
+  TEST_fff_f (fma, 0x1.fffffep+127, 2.0, -0x1.fffffep+127, 0x1.fffffep+127);
+#endif
+#if defined (TEST_DOUBLE) && DBL_MANT_DIG == 53
+  TEST_fff_f (fma, 0x1.7fp+13, 0x1.0000000000001p+0, 0x1.ffep-48, 0x1.7f00000000001p+13);
+  TEST_fff_f (fma, 0x1.fffp+0, 0x1.0000000000001p+0, -0x1.fffp+0, 0x1.fffp-52);
+  TEST_fff_f (fma, 0x1.fffffffffffffp+1023, 0x1.001p+0, -0x1.fffffffffffffp+1023, 0x1.fffffffffffffp+1011);
+  TEST_fff_f (fma, -0x1.fffffffffffffp+1023, 0x1.fffffffffffffp+0, 0x1.fffffffffffffp+1023, -0x1.ffffffffffffdp+1023);
+  TEST_fff_f (fma, 0x1.fffffffffffffp+1023, 2.0, -0x1.fffffffffffffp+1023, 0x1.fffffffffffffp+1023);
 #endif
 
   END (fma);
--- libc/sysdeps/ieee754/dbl-64/s_fmaf.c.jj	2010-10-12 07:36:10.000000000 +0200
+++ libc/sysdeps/ieee754/dbl-64/s_fmaf.c	2010-10-12 16:56:19.000000000 +0200
@@ -39,7 +39,7 @@ __fmaf (float x, float y, float z)
   fesetround (FE_TOWARDZERO);
   /* Perform addition with round to odd.  */
   u.d = temp + (double) z;
-  if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0xff)
+  if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
     u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
   feupdateenv (&env);
   /* And finally truncation with round to nearest.  */
--- libc/sysdeps/ieee754/dbl-64/s_fma.c.jj	2010-10-12 15:44:44.000000000 +0200
+++ libc/sysdeps/ieee754/dbl-64/s_fma.c	2010-10-12 20:52:40.000000000 +0200
@@ -0,0 +1,140 @@
+/* Compute x * y + z as ternary operation.
+   Copyright (C) 2010 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, write to the Free
+   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+   02111-1307 USA.  */
+
+#include <float.h>
+#include <math.h>
+#include <fenv.h>
+#include <ieee754.h>
+
+/* This implementation uses rounding to odd to avoid problems with
+   double rounding.  See a paper by Boldo and Melquiond:
+   http://www.lri.fr/~melquion/doc/08-tc.pdf  */
+
+double
+__fma (double x, double y, double z)
+{
+  union ieee754_double u, v, w;
+  int adjust = 0;
+  u.d = x;
+  v.d = y;
+  w.d = z;
+  if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
+			>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0)
+      || __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
+      || __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
+      || __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0))
+    {
+      /* If x or y or z is Inf/NaN or if fma will certainly overflow,
+	 compute as x * y + z.  */
+      if (u.ieee.exponent == 0x7ff
+	  || v.ieee.exponent == 0x7ff
+	  || w.ieee.exponent == 0x7ff
+	  || u.ieee.exponent + v.ieee.exponent
+	     > 0x7ff + IEEE754_DOUBLE_BIAS)
+	return x * y + z;
+      if (u.ieee.exponent + v.ieee.exponent
+	  >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG)
+	{
+	  /* Compute 1p-53 times smaller result and multiply
+	     at the end.  */
+	  if (u.ieee.exponent > v.ieee.exponent)
+	    u.ieee.exponent -= DBL_MANT_DIG;
+	  else
+	    v.ieee.exponent -= DBL_MANT_DIG;
+	  /* If x + y exponent is very large and z exponent is very small,
+	     it doesn't matter if we don't adjust it.  */
+	  if (w.ieee.exponent > DBL_MANT_DIG)
+	    w.ieee.exponent -= DBL_MANT_DIG;
+	  adjust = 1;
+	}
+      else if (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
+	{
+	  /* Similarly.
+	     If z exponent is very large and x and y exponents are
+	     very small, it doesn't matter if we don't adjust it.  */
+	  if (u.ieee.exponent > v.ieee.exponent)
+	    {
+	      if (u.ieee.exponent > DBL_MANT_DIG)
+		u.ieee.exponent -= DBL_MANT_DIG;
+	    }
+	  else if (v.ieee.exponent > DBL_MANT_DIG)
+	    v.ieee.exponent -= DBL_MANT_DIG;
+	  w.ieee.exponent -= DBL_MANT_DIG;
+	  adjust = 1;
+	}
+      else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
+	{
+	  u.ieee.exponent -= DBL_MANT_DIG;
+	  v.ieee.exponent += DBL_MANT_DIG;
+	}
+      else
+	{
+	  v.ieee.exponent -= DBL_MANT_DIG;
+	  u.ieee.exponent += DBL_MANT_DIG;
+	}
+      x = u.d;
+      y = v.d;
+      z = w.d;
+    }
+  /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
+#define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
+  double x1 = x * C;
+  double y1 = y * C;
+  double m1 = x * y;
+  x1 = (x - x1) + x1;
+  y1 = (y - y1) + y1;
+  double x2 = x - x1;
+  double y2 = y - y1;
+  double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
+
+  /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
+  double a1 = z + m1;
+  double t1 = a1 - z;
+  double t2 = a1 - t1;
+  t1 = m1 - t1;
+  t2 = z - t2;
+  double a2 = t1 + t2;
+
+  fenv_t env;
+  feholdexcept (&env);
+  fesetround (FE_TOWARDZERO);
+  /* Perform m2 + a2 addition with round to odd.  */
+  u.d = a2 + m2;
+  if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
+    u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
+  feupdateenv (&env);
+
+  /* Add that to a1.  */
+  a1 = a1 + u.d;
+
+  /* And adjust exponent if needed.  */
+  if (__builtin_expect (adjust, 0))
+    a1 *= 0x1p53;
+
+  return a1;
+}
+#ifndef __fma
+weak_alias (__fma, fma)
+#endif
+
+#ifdef NO_LONG_DOUBLE
+strong_alias (__fma, __fmal)
+weak_alias (__fmal, fmal)
+#endif
--- libc/sysdeps/i386/i686/multiarch/s_fma.c.jj	2010-05-03 20:18:36.000000000 +0200
+++ libc/sysdeps/i386/i686/multiarch/s_fma.c	2010-10-12 20:38:24.000000000 +0200
@@ -33,4 +33,4 @@ weak_alias (__fma, fma)
 # define __fma __fma_ia32
 #endif
 
-#include <math/s_fma.c>
+#include <sysdeps/ieee754/dbl-64/s_fma.c>
--- libc/sysdeps/x86_64/multiarch/s_fma.c.jj	2009-09-03 12:12:45.000000000 +0200
+++ libc/sysdeps/x86_64/multiarch/s_fma.c	2010-10-12 17:36:18.000000000 +0200
@@ -1,5 +1,5 @@
 /* FMA version of fma.
-   Copyright (C) 2009 Free Software Foundation, Inc.
+   Copyright (C) 2009, 2010 Free Software Foundation, Inc.
    Contributed by Intel Corporation.
    This file is part of the GNU C Library.
 
@@ -40,4 +40,4 @@ weak_alias (__fma, fma)
 # define __fma __fma_sse2
 #endif
 
-#include <math/s_fma.c>
+#include <sysdeps/ieee754/dbl-64/s_fma.c>
--- libc/sysdeps/ieee754/ldbl-opt/s_fma.c.jj	2009-05-16 19:23:39.000000000 +0200
+++ libc/sysdeps/ieee754/ldbl-opt/s_fma.c	2010-10-12 20:39:13.000000000 +0200
@@ -1,5 +1,5 @@
 #include <math_ldbl_opt.h>
-#include <math/s_fma.c>
+#include <sysdeps/ieee754/dbl-64/s_fma.c>
 #if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
 compat_symbol (libm, __fma, fmal, GLIBC_2_1);
 #endif
--- libc/sysdeps/ieee754/ldbl-128/s_fma.c.jj	2010-10-12 20:40:47.000000000 +0200
+++ libc/sysdeps/ieee754/ldbl-128/s_fma.c	2010-10-12 20:43:51.000000000 +0200
@@ -0,0 +1,50 @@
+/* Compute x * y + z as ternary operation.
+   Copyright (C) 2010 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, write to the Free
+   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+   02111-1307 USA.  */
+
+#include <math.h>
+#include <fenv.h>
+#include <ieee754.h>
+
+/* This implementation relies on long double being more than twice as
+   precise as double and uses rounding to odd in order to avoid problems
+   with double rounding.
+   See a paper by Boldo and Melquiond:
+   http://www.lri.fr/~melquion/doc/08-tc.pdf  */
+
+double
+__fma (double x, double y, double z)
+{
+  fenv_t env;
+  /* Multiplication is always exact.  */
+  long double temp = (long double) x * (long double) y;
+  union ieee854_long_double u;
+  feholdexcept (&env);
+  fesetround (FE_TOWARDZERO);
+  /* Perform addition with round to odd.  */
+  u.d = temp + (long double) z;
+  if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff)
+    u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0;
+  feupdateenv (&env);
+  /* And finally truncation with round to nearest.  */
+  return (double) u.d;
+}
+#ifndef __fma
+weak_alias (__fma, fma)
+#endif

	Jakub


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